{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:U5ET6TN2BDDBDET5YRLFQB6FVY","short_pith_number":"pith:U5ET6TN2","schema_version":"1.0","canonical_sha256":"a7493f4dba08c611927dc4565807c5ae17f39b07b36157281ccd0d0b86a3ee18","source":{"kind":"arxiv","id":"1212.4442","version":1},"attestation_state":"computed","paper":{"title":"Polytopes associated to Dihedral Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.CO","authors_text":"Andreas Paffenholz, Barbara Baumeister, Benjamin Nill, Christian Haase","submitted_at":"2012-12-18T17:47:14Z","abstract_excerpt":"In this note we investigate the convex hull of those $n \\times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein polytope, and we determine the Ehrhart $h^*$-vector."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.4442","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-18T17:47:14Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"29912b9db2c530611df16a823f6b8ed15c2c36cf250e81505f1318e0e822a4c0","abstract_canon_sha256":"9f12a7793a60d78c94e41b32ed96852894e76a8a10a97d2ae338ce6ea07e350d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:12.969025Z","signature_b64":"pIaF0egJAHNcdjyjCFLoJq/0hOxYT/3/OYWXKVQijjBWWD5vBPTV8jf1IL+IOQlEItvl08tmELAtY7LQ4Y1vDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7493f4dba08c611927dc4565807c5ae17f39b07b36157281ccd0d0b86a3ee18","last_reissued_at":"2026-05-18T03:38:12.968081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:12.968081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polytopes associated to Dihedral Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.CO","authors_text":"Andreas Paffenholz, Barbara Baumeister, Benjamin Nill, Christian Haase","submitted_at":"2012-12-18T17:47:14Z","abstract_excerpt":"In this note we investigate the convex hull of those $n \\times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein polytope, and we determine the Ehrhart $h^*$-vector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4442","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.4442","created_at":"2026-05-18T03:38:12.968238+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.4442v1","created_at":"2026-05-18T03:38:12.968238+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4442","created_at":"2026-05-18T03:38:12.968238+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5ET6TN2BDDB","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5ET6TN2BDDBDET5","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5ET6TN2","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY","json":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY.json","graph_json":"https://pith.science/api/pith-number/U5ET6TN2BDDBDET5YRLFQB6FVY/graph.json","events_json":"https://pith.science/api/pith-number/U5ET6TN2BDDBDET5YRLFQB6FVY/events.json","paper":"https://pith.science/paper/U5ET6TN2"},"agent_actions":{"view_html":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY","download_json":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY.json","view_paper":"https://pith.science/paper/U5ET6TN2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.4442&json=true","fetch_graph":"https://pith.science/api/pith-number/U5ET6TN2BDDBDET5YRLFQB6FVY/graph.json","fetch_events":"https://pith.science/api/pith-number/U5ET6TN2BDDBDET5YRLFQB6FVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY/action/storage_attestation","attest_author":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY/action/author_attestation","sign_citation":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY/action/citation_signature","submit_replication":"https://pith.science/pith/U5ET6TN2BDDBDET5YRLFQB6FVY/action/replication_record"}},"created_at":"2026-05-18T03:38:12.968238+00:00","updated_at":"2026-05-18T03:38:12.968238+00:00"}